母线作图
几何画板及绘图内容加载中,请稍等……
本范例展示了折纸活动中发现的母线现象。核心数学概念包括相似三角形和角平分线。通过使用Polygon, Point, Segment, AngularBisector等GeoGebra命令,可以构造出复杂的几何图形。适合用于几何作图的教学演示。
GeoGebra 命令及参数
Polygon(A, B, 4) → veelhoek1, a, b, c, d, C, DPolygon(I, J, 4) → veelhoek3, i, j, k, l, K, LPoint(d) → QPoint(b) → RSegment(Q, R) → rPoint(k) → UPoint(j) → VSegment(U, V) → tAngularBisector(d, r) → b_1, c_1AngularBisector(r, b) → d_1, e_1AngularBisector(r, a) → f_1, g_1AngularBisector(c, r) → h_1, i_1Intersect(e_1, c) → A_1Segment(A_1, R) → j_1Intersect(i_1, d) → B_1Intersect(i_1, b) → C_1Segment(B_1, C_1) → k_1Intersect(c_1, c) → D_1Segment(Q, D_1) → l_1Intersect(b_1, a) → E_1Segment(Q, E_1) → m_1Intersect(d_1, a) → F_1Segment(F_1, R) → n_1Intersect(f_1, d) → G_1Intersect(f_1, b) → H_1Segment(G_1, H_1) → p_1Intersect(j_1, l_1) → I_1Intersect(j_1, k_1) → J_1Intersect(k_1, l_1) → K_1Intersect(m_1, p_1) → L_1Intersect(n_1, p_1) → M_1Intersect(m_1, n_1) → N_1AngularBisector(t, k) → e, fAngularBisector(t, j) → g, hAngularBisector(t, l) → s, q_1AngularBisector(t, i) → r_1, s_1Intersect(s, k) → GIntersect(s, i) → HSegment(G, H) → t_1Intersect(g, i) → SSegment(S, V) → a_2Intersect(e, l) → TSegment(T, U) → b_2Intersect(f, j) → O_1Segment(U, O_1) → c_2Intersect(h, k) → P_1Segment(P_1, V) → d_2Intersect(r_1, l) → Q_1Intersect(r_1, j) → R_1Segment(Q_1, R_1) → e_2Intersect(g, l) → S_1Segment(S_1, V) → f_2Intersect(e, i) → T_1Segment(U, T_1) → g_2Intersect(t_1, g_2) → U_1Intersect(e_2, g_2) → V_1Intersect(f_2, g_2) → W_1Intersect(t_1, f_2) → Z_1Intersect(e_2, f_2) → A_2Intersect(c_2, d_2) → B_2Intersect(b_2, e_2) → C_2Intersect(t_1, b_2) → D_2Intersect(t_1, e_2) → E_2Intersect(t_1, a_2) → F_2Intersect(a_2, e_2) → G_2Point(c) → H_2Point(a) → I_2Segment(H_2, I_2) → h_2Point(d) → J_2Point(b) → K_2Segment(J_2, K_2) → i_2Intersect(b, c) → L_2Intersect(a, d) → M_2Segment(L_2, M_2) → j_2Point(k) → N_2Point(l) → P_2Point(j) → Q_2Segment(P_2, Q_2) → l_2Intersect(k, l) → R_2Intersect(i, j) → S_2Segment(R_2, S_2) → m_2Intersect(j, k) → T_2Intersect(i, l) → U_2Segment(T_2, U_2) → n_2Intersect(c, d) → V_2Intersect(a, b) → W_2Segment(V_2, W_2) → p_2Intersect(i, l) → Z_2Intersect(k, l) → A_3Ray(Z_2, A_3) → q_2Line(U, V) → r_2Intersect(i, j) → B_3Ray(Z_2, B_3) → s_2Intersect(r_2, q_2) → C_3Intersect(r_2, s_2) → OSegment(C_3, A_3) → mSegment(C_3, U) → nSegment(V, O) → pSegment(O, B_3) → qSegment(A_2, O) → a_1Segment(U_1, C_3) → t_2Intersect(j, e_2) → PSegment(P, O) → a_3Intersect(k, t_1) → WSegment(C_3, W) → b_3OrthogonalLine(E_2, t) → c_3Intersect(c_3, t) → ZCircle(E_2, Z) → d_3OrthogonalLine(B_2, t) → e_3Intersect(e_3, t) → D_3Circle(B_2, D_3) → f_3OrthogonalLine(U_1, t) → g_3Intersect(g_3, t) → E_3OrthogonalLine(U_1, l) → i_3Intersect(i_3, l) → F_3OrthogonalLine(D_2, k) → j_3Intersect(j_3, k) → G_3Ray(Q, R) → l_3Intersect(c, d) → H_3Intersect(b, c) → I_3Ray(H_3, I_3) → m_3Intersect(l_3, m_3) → J_3Segment(I_3, J_3) → n_3Segment(J_3, R) → p_3Intersect(b, k_1) → K_3Segment(K_3, J_3) → q_3OrthogonalLine(K_1, c) → r_3Intersect(r_3, c) → L_3Circle(K_1, L_3) → s_3Intersect(a, b) → M_3Intersect(a, d) → N_3Line(M_3, N_3) → t_3Line(R, Q) → a_4Intersect(t_3, a_4) → O_3Segment(O_3, Q) → b_4Segment(O_3, N_3) → c_4Intersect(d, p_1) → P_3Segment(O_3, P_3) → d_4OrthogonalLine(M_1, b) → e_4Intersect(e_4, b) → Q_3Circle(M_1, Q_3) → f_4OrthogonalLine(J_1, c) → g_4OrthogonalLine(L_1, a) → h_4Intersect(g_4, c) → R_3Intersect(h_4, a) → S_3Circle(J_1, R_3) → k_4Circle(L_1, S_3) → p_4OrthogonalLine(G_2, i) → i_4Intersect(i_4, i) → T_3Midpoint(k) → U_3Midpoint(i) → V_3Segment(U_3, V_3) → k_2OrthogonalLine(D_2, k) → h_3OrthogonalLine(G_2, i) → k_3Intersect(h_3, k) → W_3Intersect(k_3, i) → Z_3Circle(D_2, W_3) → q_4Circle(G_2, Z_3) → r_4OrthogonalLine(U_1, k) → j_4OrthogonalLine(A_2, i) → l_4Intersect(j_4, k) → A_4Intersect(l_4, i) → B_4Circle(U_1, A_4) → s_4Circle(A_2, B_4) → t_4
AI 绘图提示语参考
绘制一个由多个三角形和线段组成的复杂几何图形。首先绘制两个四边形,然后在四边形的边和对角线上找到中点,连接这些中点形成新的线段。接着,利用角平分线构造方法,从这些线段出发,逐步构造出更多的线段和交点,最终形成一个由多个三角形和线段交织而成的复杂图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。